Surface Waves Alter Air Entrainment During Water Entry

Abstract

When a sphere crosses an air-water interface it can entrain a significant volume of air, a process relevant to numerous naval, industrial, and environmental settings. While air entrainment through sphere impact onto quiescent baths has been extensively studied, real-world interfaces are inherently unsteady, and the influence of surface waves is less understood. In this Letter, we systematically investigate the effect of interfacial geometry on the air entrained by impacting hydrophobic spheres onto an axisymmetric wavefield. By analyzing the resulting cavity across a wide parameter space, including wave phase, driving amplitude, and frequency, we reveal that local interface deformation dramatically alters air entrainment. This effect is driven by a geometric modulation of the splash curtain, which shifts the transition between cavity closure modes. We demonstrate that the influence of the waves is fully described by the local wave slope at the radius of the sphere, which alongside the Weber number We and Bond number Bo, establishes a foundational parametric framework for predicting air entrainment and cavity metrics across highly dynamic, real-world surfaces like the open ocean.